Download Section 4.3-4.6 Section 4.4 Section 4.5 Section 4.6

Summer 2016 Math 151
Week in Review 3
courtesy: Amy Austin
(covering 4.3-4.6)
11. Find the equation of the tangent line to the graph
of f (x) = x ln x at x = e2 .
12. What is the slope of the parametric curve
x = t ln t, y = 23t at the point (0, 8)?
Section 4.5
13. A bacteria culture starts with 400 bacteria and the
population triples every 20 minutes.
Section 4.3-4.6
1. Evaluate log3 108 − log3 4
2. Express log8 x−log8
logarithm.
√
9x + 2+log8 (x+1) as a single
a.) Find an expression for the number of bacteria
after t hours.
b.) Find the number of bacteria after 2 days.
c.) When will the population reach 20,000?
3. Solve for x: log(x + 3) + log(x) = 1
4. Solve for x: y = ln(7x − 9)
5. Solve for x: ln x − ln(x + 1) = ln 2 + ln 3
6. Find the inverse of f (x) = e6x−3
7. Find lim [log(2x − 1) − log(3x + 6)]
x→∞
√
8. Find the value of ln e3
9. What is the domain of f (x) = ln(4 − x2 )?
Section 4.4
10. Differentiate each function:
a.) f (t) = cos2 t(ln t)
14. A curve that passes through the point (0, 25) has
the property that the slope at every point (x, y) is
eight times the y coordinate. Find the equation of
the curve.
15. A pie is taken from an oven, where the temperature is 450◦ , to a 75◦ room. After 15 minutes, the
temperature of the pie reads 350◦ . What will the
temperature of the pie be after 27 minutes?
Section 4.6
16. Compute the following without the aid of a calculator.
√
1
3
b.) arccos(− √ )
a.) arcsin
2
2
√
1
2
)
d.) arctan √
c.) sin−1 (−
2
3
3
f.) sin(arcsin 2)
e.) cot arccos(− )
5
2π
5π
g.) arccos(cos( ))
h.) arctan(tan
)
3
4
1
11π
))
j.) sin(2 arccos( ))
i.) arcsin(sin((
6
3
b.) f (x) = ln(sin 2x)
17. Find the derivative of y = arctan(1 − x)
c.) h(x) = ln(ln 3x)
18. Find the equation of the tangent line to the graph
x
of y = arcsin at x = −1.
2
d.) f (x) = log5 (e10x )
e.) f (x) =
3tan(7x)
f.) y = xsin x
19. What is the domain of f (x) = arcsin(2x − 1)? Of
arctan(2x − 1)?
20. cos(arctan x) is equivalent to what?